I. Load data

In this section, I load data for the baseline calibration using the linear and linear quadratic cost models.

params value concept units
alpha 1625836.98 Demand model : intercept USD
beta 1563.75 Demand model : coefficient USD/metric ton of biomass
r 0.20 Intrinsic growth rate unitless
k 20226.00 Carrying capacity (in metric tons) metric tons of biomass
sigma 0.00 Catchability % of biomass/vessel trip
avg_cost 14386.69 Average cost per vessel trip at historical value USD/vessel trip
W_high 3.75 Quadratic cost parameter - Quadratic cost function USD vessel trip\(^{-2}\)
fixed_cost 13811222.14 Fixed cost - Quadratic cost function USD
W1 13012.59 Linear cost parameter - Linear quadratic cost function USD/vessel trip
W2 0.75 Quadratic cost parameter - Linear quadratic cost function USD vessel trip\(^{-2}\)
age 4.50 Age of farmed totoaba Years
gamma 1354.25 Demand model : substitutable good coefficient USD/metric ton of biomass
v 89929.92 Unit cost of farming USD/metric ton of biomass
i_r 0.10 Interest rate %
c 0.00 Unit cost of trading USD/ metric ton of biomass

II. Define functions

Define function where variable is either x i.e population stock, or s i.e price paid to poachers. All the parameters take default values specified in the global environment.

  • growth(x, ...) : logistic growth function, yields growth of population (in metric tons)

  • pt_harvest(x,...) : harvest (in metric tons) when trader is price taker

  • monop_harvest(x, ...): harvest (in metric tons) when trader is a monopolist

  • monop_harvest_lq(x, ...): harvest (in metric tons) when trader is a monopolist and cost structure is linear quadratic

  • cournot_harvest(x, ...), bertrand_harvest(x, ...): harvest (in metric tons) when trader and farmer compete in Cournot, i.e, set quantities strategically, and Bertrand, i.e, set prices strategically.

  • cournot_harvest_lq(x, ...), bertrand_harvest_lq(x, ...) : harvest (in metric tons) when trader and farmer compete in Cournot i.e, set quantities strategically, and Bertrand i.e, set prices strategically and cost structure is linear quadratic

  • price_poachers_cournot(x, ...), price_poachers_bertrand(x, ...): price paid to poachers (in USD/metric tons) when trader and farmer compete in Cournot and Bertrand

  • cournot_farmed(s, ...), bertrand_farmed(s, ...): quantity farmed (in metric tons) when trader and farmer compete in Cournot and Bertrand

III. Generate results

Generate results saved at ~/data/outputs/results_all_models.csv :

  • Set cost variables using W_lq_new: each row corresponds to a cost parameter \(W\), \(W_1\) and \(W_2\)

Graph outputs :

A. Understanding the impact of different values of W1 and W2

To understand the impact of different \(W_1\) & \(W_2\) divides :

Clearly, the choice of \(W_1\) and \(W_2\) is important with respect to the anticipated equilibrium in the vertical monopoly case : with a linear-quadratic cost function, we no longer can say the monopoly will achieve a healthy steady state population. The results in the post intervention world are robust to the cost specification, and guarantee population increases in the quantity adjustment scenario, while population may marginally diminish in the price setting scenario.

B. Graph with prefered specification

First, illustrate the new equilibria with the same \(W\) = 3.7465338 value and the prefered solution for \(W_1\) and \(W_2\) (e.g 13012.59, 0.75) in the linear quadratic cost of effort specification.

Define bio-economic performance by combining population variables (stock and harvest) with price and profit data from economic model.

tinytable_b9e6utjuf11k3itllqxb
Bioeconomic performance - with baseline specification
Scenario Poached harvest (in mt) Farmed harvest (in mt) Steady state population (in mt) Retail price (in USD/ton of buche) Retail price of 500g buche (in USD) Price paid to poacher (in USD/ton of buche) Poacher price of 500g buche (in USD) Illegal profit (in million USD) Farming profit (in million USD) Fishing profit (in million USD) Aggregate profit (in million USD) Aggregate profit change (in million USD) Farming profit change (in million USD) Illegal profit change (in million USD) Fishing profit change (in million USD) Variation in ss. pop. Poaching change (%)
Vertical Monopoly 509.64 0.00 17259.0 828894.3 21302.583 31951.60 821.1560 406.15 0.00 8.14 414.29 12.61 0.00 6.07 6.54 -0.16% 0.76%
Quantity adjustment 369.87 330.94 18182.0 599279.2 15401.476 20894.42 536.9866 213.93 171.26 3.86 389.05 -12.63 171.26 -186.15 2.26 5.18% -26.88%
Price setting 520.27 425.30 17184.0 236298.3 6072.866 32903.89 845.6299 105.82 70.71 8.56 185.09 -216.59 70.71 -294.26 6.96 -0.59% 2.86%
Vertical Monopoly - LQ cost 505.81 0.00 17286.0 834873.3 21456.245 43909.71 1128.4797 400.08 0.00 1.60 401.68 0.00 0.00 0.00 0.00 0% 0%
Quantity adjustment - LQ cost 362.46 334.15 18228.0 606518.8 15587.534 39717.45 1020.7385 205.44 174.60 0.74 380.78 -20.90 174.60 -194.63 -0.86 5.45% -28.34%
Price setting - LQ cost 536.94 432.53 17257.5 200446.5 5151.475 43506.01 1118.1043 84.27 57.26 4.41 145.94 -255.74 57.26 -315.81 2.81 -0.16% 6.15%

Table for manuscript :

tinytable_qu2q108zuxu3apmud0re
Bioeconomic performance
Scenario Poached harvest (in mt) Farmed harvest (in mt) Steady state population (in mt) Illegal profit (in million USD) Farming profit (in million USD) Fishing profit (in million USD) Aggregate profit (in million USD) Illegal profit change (in million USD) Variation in ss. pop. Poaching change (%)
Vertical Monopoly 505.81 0.00 17286.0 400.08 0.00 1.60 401.68 0.00 0% 0%
Quantity adjustment 362.46 334.15 18228.0 205.44 174.60 0.74 380.78 -194.63 5.45% -28.34%
Price setting 536.94 432.53 17257.5 84.27 57.26 4.41 145.94 -315.81 -0.16% 6.15%